We analyze an algorithm for the misregistered trade-off heterocorrelation filter (HCF) using nonlinear transformation methods. This HCF consists of a matched filter modified by a transmittance function that has been optimized for the metric peak-to-mismatched energy. We find that this algorithm employs a new form of the nonlinear synthetic discriminant function algorithm that generates multiple correlation peaks for both autocorrelation and heterocorrelation when the filter function is made up of functions misregistered (i.e., shifted) with respect to each other. By means of computer simulations we study the effect that the trade-off factor (β), weighting the Fourier spectrum difference, has on the autocorrelation, heterocorrelation, and cross-correlations for centered inputs when the matched filter is used as the basic filter. We find that as β increases, the difference between the autocorrelation and heterocorrelation peak intensities diminishes and reaches a minimum value when β approaches 1. Furthermore, we find that for exactly registered (i.e., unshifted) images used to make up the HCF, there is only one order of autocorrelation peak and only one order of heterocorrelation peak; however, as the amount of misregistration increases, both the autocorrelation and heterocorrelation peaks split into many orders and their positions are displaced relative to each other. The amount of shift between successive autocorrelation and heterocorrelation peaks is equal to the amount of shift in the misregistered images used to make up the filter.